1. Field of the Invention
The present invention relates to computer graphics systems and, more particularly, to a system and method for calculating a texture-mapping gradient.
2. Discussion of the Related Art
Computer graphics systems are commonly used for displaying graphical representations of objects on a two-dimensional video display screen. Current computer graphics display systems provide highly-detailed representations and are used in a variety of applications. A computer graphics display system generally comprises a central processing unit (CPU), system memory, a graphics subsystem and a video display screen.
In typical computer graphics display systems, an object to be presented on the display screen is broken down into graphics primitives. Primitives are basic components of a graphics display and may include points, lines, vectors and polygons (e.g., triangles and quadrilaterals). Typically, a hardware/software scheme is implemented to render, or draw, the graphics primitives that represent a view of one or more objects being illustrated on the display screen.
Generally, the primitives of a three-dimensional object to be rendered are defined by the host CPU in terms of primitive data. For example, when the primitive is a triangle, the host computer may define the primitive in terms of the X, Y and Z coordinates of its vertices. Additional primitive data may be used in specific applications. Rendering hardware interpolates the primitive data to compute the display screen pixels that represent each primitive.
The graphics subsystem generally includes a geometry accelerator, a rasterizer, a frame buffer controller and a frame buffer. The graphics subsystem may also include texture-mapping hardware. The geometry accelerator receives vertex data from the host CPU that defines the primitives that make up the view to be displayed. As is known, the operations of the geometry accelerator are computationally very intense. One frame of a three-dimensional (3-D) graphics display may include on the order of hundreds of thousands of primitives. To achieve state-of-the-art performance, the geometry accelerator may be required to perform several hundred million floating point calculations per second. Furthermore, the volume of data transferred between the host computer and the graphics hardware is very large. Additional data transmitted from the host computer to the geometry accelerator includes illumination parameters, clipping parameters and any other parameters needed to generate the graphics display.
As is known, a rasterizer receives data representing figures or objects and then provides the pixel-like representation of the figures. As is also known, texture-mapping involves applying one or more point elements (texels) of a texture to each point element (pixel) of the displayed portion of the object to which the texture is being mapped. Texture-mapping hardware is conventionally provided with information indicating the manner in which the texels in a texture map correspond to the pixels on the display screen that represent the object. Each texel in a texture map may be defined by s and t (and r, if three-dimensional texture map) coordinates which identify its location in the two-dimensional texture map. For each pixel, the corresponding texel or texels that map to it are accessed from the texture map, and incorporated into the final Red, Green, Blue (RGB) values generated for the pixel to represent the textured object on the display screen. As is known, in addition to two-dimensional texture maps, one-dimensional, three-dimensional, and even other-dimensional texture maps are also known. In this respect, the two-dimensional texture map has been mentioned for illustrative purposes only.
It should be understood that each pixel in an object primitive may not map in one-to-one correspondence with a single texel in the texture map for every view of the object. For example, the closer the object is to the view port represented on the display screen, the larger the object will appear. As the object appears larger on the display screen, the representation of the texture becomes more detailed. Thus, when the object consumes a fairly large portion of the display screen, a large number of pixels is used to represent the object on the display screen, and each pixel that represents the object may map in one-to-one correspondence with a single texel in the texture map, or a single texel may map to multiple pixels. However, when the object takes up a relatively small portion of the display screen, a much smaller number of pixels is used to represent the object, resulting in the texture being represented with less detail, so that each pixel may map to multiple texels. Each pixel may also map to multiple texels when a texture is mapped to a small portion of an object. Resultant texel data is calculated for each pixel that maps to more than one texel, and typically represents an average of the texels that map to that pixel.
To more particularly illustrate a conventional graphics system, reference is made to FIG. 1, which is a diagram illustrating a graphics pipeline 10 as is known. It should be noted at the outset that there are a variety of alternative manners to illustrate the graphics pipeline 10 illustrated in FIG. 1, and that the diagram of FIG. 1 is presented for illustration only.
As illustrated, a host computer 20 typically communicates with the graphics hardware across a high-speed bus, such as an AGP (accelerated graphics port) bus or a PCI (peripheral component interconnect) bus. A host interface 22 is typically provided at the front end of the graphics hardware to interface with the high-speed bus. A format block 24 is provided downstream of the host interface 22. One or more geometry accelerators 26 and 27, and one or more rasterizers 30 and 31 are provided downstream of the format block 24. Information produced or generated by each geometry accelerator is broadcast to all downstream rasterizers. The operation of geometry accelerators and rasterizers, and methods/configurations for operating multiples of these components are known, and therefore need not be described herein.
Downstream of the rasterizers 30 and 31 are texture-mapping hardware 34, a fragment processor 36, the Z-buffer 38, and blend hardware 40. The function and operation of each of these components are known and need not be described herein. As is known, however, texture-mapping hardware systems typically include a local memory subsystem 50 that stores data representing a texture associated with the object being rendered.
Downstream of the texture-mapping hardware are subsystems including display composition 52, display timing 54, digital-to-analog converter (DAC) 56, and a display 58. As is known, the display composition hardware 52 processes different object/primitive layers to determine the color of a given pixel to be displayed.
Texture mapping involves applying one or more texture map elements, or texels, of a texture to each pixel of the displayed portion of the object to which the texture is being mapped. Each texel in a texture map is defined by coordinates (generally two or more spatial coordinates, e.g., s, t, and, sometimes, a homogeneous texture effect parameter q) which identify its location in the texture map (two-dimensional or greater). For each pixel, the corresponding texel(s) that maps to the pixel is accessed from the texture map via the texel coordinates (e.g., s, t, q of an orthogonal coordinate system) associated with that pixel and is incorporated into the final R, G, B values generated for the pixel to represent the textured object on the display screen. It should be understood that each pixel in an object primitive may not map in a one-to-one correspondence with a single texel in the texture map for every view of the object.
Texture-mapping systems typically store data in memory representing a texture associated with the object being rendered. As indicated above, a pixel may map to multiple texels. If it is necessary for the texture-mapping system to read a large number of texels that map to a pixel from memory to generate an average value, then a large number of memory reads and the averaging of many texel values would be required, which would undesirably consume time and degrade system performance.
To overcome this problem, a well-known scheme has been developed that involves the creation of a series of MIP (multum in parvo, or many things in a small place) maps for each texture, and storing the MIP maps of the texture associated with the object being rendered in memory. A set of MIP maps for a texture includes a base map that corresponds directly to the texture map as well as a series of related filtered maps, wherein each successive map is reduced in size by a factor of two in each of the texture map dimensions (s, t, and r). In a sense, the MIP maps represent different resolutions of the texture map.
An illustrative example of a set of MIP maps is shown in FIG. 2. In this simplified example, the MIP maps of FIG. 2 are two dimensional (s, t) and include a base map 64a (the reference) that is eight-by-eight texels 65 in size, as well as a series of maps 64b, 64c, and 64d that are respectively four-by-four texels 65, two-by-two texels 65, and one texel 65 in size. The four-by-four map 64b is generated by box filtering (downsampling) the base map 64a. With box filtering, each texel 65 in the map 64b corresponds to an equally-weighted average of four adjacent texels 65 in the base map 64a. Further, the two-by-two map 64c is similarly generated by box filtering map 64b. Finally, the single texel 65 in map 64d is generated by box averaging the four texels 65 in map 64c. 
The computer graphics system determines which MIP map 64 in a series of MIP maps 64a-64d to access in order to provide the appropriate texture data for a particular pixel 73 (see FIG. 3) based upon the number of texels 65 to which the pixel 73 maps. For example, if the pixel 73 maps in a one-to-one correspondence with a single texel 65 in the texture map, then the base map 64a is accessed. However, if the pixel maps to four, sixteen, or sixty-four texels, then the maps 64b, 64c and 64d are respectively accessed because those maps respectively store texel data representing an average of four, sixteen, and sixty-four texels 65 in the texture map.
In order to determine the number of texels 65 to which a pixel 73 maps so that the appropriate MIP map 64 can be accessed, gradients (mathematical derivatives) of the various texel coordinates with respect to screen coordinates are computed. In this regard, gradient values ∂i/∂x, ∂i/∂y, where i is s or t in the texel domain and where x, y are screen coordinates, are calculated. These gradients reflect the rate of change of texture coordinates 65 relative to pixel coordinates 73. Often, a single gradient is allocated to each pixel 73 by selecting the largest gradient.
Prior methods for determining the gradients generally rely on using some form of either a linear-difference formula or a central-difference formula. The former is more popular than the latter due, in part, to its simplicity and ease of implementation. With a linear-difference formula, each gradient derivative is essentially equal to an old gradient derivative plus a constant. Given the gradient at the vertices of a triangular primitive 71, the gradients along the edges as well as along the spans 72 of the primitive 71 are linearly approximated. When a central-difference formula is employed, each gradient derivative is essentially equal to a weighted sum of nearby gradient derivatives. Although useful to an extent, these methods for calculating gradients are inaccurate, especially for highly spatially perspected rendered primitives 71. The larger the primitive 71, the more spatially-perspected and the greater the error. Furthermore, these methods are computationally complex relative to the degree of accuracy that they accomplish.
Another prior approach includes the calculation of gradient values by the geometry accelerator. Generally, this approach is undesirable because it places an additional computational load on the geometry accelerator, which already bears a significant computational load.
Yet another prior approach includes the calculation of gradient values as part of the scan-conversion process, within the rasterizer. Under this approach, gradient values are created by calculating texel values of adjacent pixels. That is, as the scan converter steps down one side of a triangle primitive, processing each successive scan line, gradient values are calculated for each pixel by calculating difference (or delta) values of a current pixel with an adjacent pixel on the same scan line and an adjacent pixel on the next scan line. This approach is undesirable because it adds hardware and complexity to the rasterizer.